PAM3012: Problem Set ONE – Hints & Solutions

1. When you enter a dark room on a bright day, it takes an appreciable interval of time before you can see properly. Which of the visual processes is responsible for this effect?

Brightness adaptation

2. How does the effect described in question 1 affect the viewing conditions for radiographic displays?

Hints:

· Effects simultaneous contrast, therefore the perceived intensity of structures within an image

· Brightness discrimination, there the perceived contrast of the image

· Mach bands: perceived modification of brightness at the edges of an object

3. Describe the function of rods and cones

· Retina contains two types of photoreceptors, rods and cones.

· Convert optical energy into an electrical signals with propagate along the optical nerve

· Rod are not sensitive to colour.

· 3 different types of cones provide colour vision

· Rods are far more sensitive to low light levels, therefore responsible for night vision

· Cones have better frequency response

· Highest density of cones at fovea, cones are responsible of high resolution vision

4. How does bit depth affect the appearance of a digital image?

Hints:

· Affects the number of available grey-levels

· Contrast resolution

· Can effect spatial resolution – depends on image properties (see section on Isopreference curves).

5. Discuss the trade-offs incurred when reducing the sensor size of an array detector.

Hints:

· Reducing sensor size increases spatial resolution

· However reducing the area of each sensor element reduces the number of photons captured per pixel, reducing SNR.

6. Explain why the highest density of cones is found at the fovea

· The fovea defines the centre of the retina, and is the region of highest visual acuity.

· The fovea is directed towards whatever object you wish to study most closely

· In the fovea there are almost exclusively cones, and they are at their highest density.

7. When viewed from the corner of your eye a computer monitor or television screen may appear to flicker. Explain this with reference to the distribution of image receptors on the retina.

Hints:

· When ‘look out of the corner of your eye’ the image is focused away from the fovea

· Periphery of retina is dominated with rods

· Rods have a lower frequency response

8. With regards to your answer to the previous question, explain how you answer relates to the relative sensitivities of rods and cones.

Hints:

· Refer to lecture notes.

9. Thinking purely in geometric terms, estimate the smallest dot that the eye can discern on a page 0.2m away from the eye.

(Assume that the visual system ceases to detect the dot when the image of the dot on the fovea becomes smaller than the diameter of one receptor. Also assume that the fovea is a square array detector 1.5 X 1.5 mm and that the receptors are distributed uniformly through this array.)

Hints:

· From density calculate radius of 1 cone 200,000 mm^-2

ð 5X10^-6 m² √(5X10^-6)=2.2 microns

· Assume image of smallest resolvable dot on retina is the same size as a cone

· Using similar triangles: 2.2x10^-6/14x10^-3 = radius of dot/0.2

· 0.2 x (2.2x10^-6/14x10^-3 ) = radius of dot in metres

10. A CCD camera chip has dimensions 7 X 7 mm, and has 1024 X 1024 elements. The camera is focused on a flat area 0.5m away using a 35 mm lens. How many line pairs per mm will the camera be able to resolve?

(Hint: A 35 mm lens has a focal distance of 35 mm; Substitute the geometric model of the eye with the lens system described in the question.)

Hint:

· Sensor element size = 7 microns

· Using similar triangles; minimum resolvable line pair separation = 0.2 mm

· Therefore line pairs per mm = 5